Is it permissible to inquire about another young man for the purpose of marriage, given the existence of an initial approval for a first suitor, before the engagement becomes official?

If there was no compatibility with the first suitor, and no inclination or closeness developed between you, then it is permissible for another person to propose to you. This does not fall under the prohibition of proposing over an existing proposal. That is because the prohibition only applies when there is closeness and inclination between the two parties. The Prophet (peace be upon him) proposed on behalf of Usamah ibn Zayd for Fatimah bint Qais after Abu Jahm and Mu'awiyah had proposed to her, because she had not accepted either of them. If the other suitor has good qualities, then accepting him is more appropriate. And since smoking is forbidden and entails many harms, the fact that the first young man is a smoker calls for preferring the other over him.